The present invention relates to digital to analog converters (DACs). More particularly, this invention relates to circuits and methods for providing a split-core DAC that is at least partially insensitive to the effects of error gradients.
The general purpose of a DAC is to transform digital input signals into analog output voltages. In other words, a DAC takes the binary bits of a digital input signal, which originate from a computer or other type of discrete circuitry, and converts the digital input signal into an analog output voltage that can be used to drive analog devices (e.g., motor controllers or audio circuitry).
There are several types of DACs that are well known and are capable of converting digital input signals into analog output voltages. An example of a commonly used DAC is the binary-weighted resistor DAC, which uses N binary-weighted resistors (where N is the number of bits of a digital signal to be converted). This type of DAC is logically simple to implement, however, it is typically not the most practical type of converter to use because the range of resistor values often becomes very large. In particular, accurate resistors across the range of resistor values become difficult to fabricate as the resolution of the binary-weighted resistor DAC increases (i.e., as N increases).
Another commonly used DAC is the R-2R resistor ladder DAC. The R-2R resistor ladder DAC uses an R-2R ladder to produce the currents that are inputted into a summing amplifier. Unlike the binary-weighted resistor DAC, however, the range of resistor values used in an R-2R ladder DAC is not a function of the DAC's resolution. Therefore, unlike with the binary-weighted resistor DAC, the problem of often requiring a large range of resistor values is not present. The R-2R ladder DAC, however, does not guarantee monotonicity, which may be particularly important in applications such as control systems. In other words, as the digital input signal to be converted increases in value, the analog output voltage is not guaranteed to also increase. Similarly, a decrease in the digital input signal does not guarantee a decrease in the analog output voltage of the R-2R ladder DAC.
A third type of commonly used DAC, which relates more specifically to the present invention and is explained in greater detail below, is the resistor string DAC. The resistor string DAC uses a resistor string (voltage divider) network to generate a set of analog output voltages through sequential voltage taps. Moreover, resistor string DACs use one of the simplest architectures, utilizing a string of ideally identical resistors connected in series between two reference voltages (e.g., a DAC reference voltage, Vref, and ground).
The resistor string of a resistor string DAC includes 2N series connected resistors, where again, N represents the resolution of the DAC, or the number of bits in the digital input signal to be converted. Assuming identical resistors, the resistor string divides the reference voltage, Vref, into 2N equally spaced voltages. The junctions (or nodes) in between each pair of connected resistors provide voltage taps through, for example, controlled switches corresponding to particular digital input signals. The respective voltage levels of these voltage taps vary according to their location relative to the reference voltages (e.g., Vref and ground).
The analog output voltage in a resistor string DAC is obtained by using one or more switches to connect the selected voltage tap to the DAC output. Persons skilled in the art will appreciate that the number of switches necessary to provide the analog output voltage depends on the type of decoder being utilized. The switches of a resistor string DAC can be controlled, for example, using an N:2N decoder that uses the binary bits of the digital signal to select one of 2N available switches to be closed, allowing the desired voltage level to be passed, or transmitted, as the analog output voltage of the resistor string DAC. Other types of decoders, however, may also be used that require, for example, greater than 2N switches. For example, a tree decoder may be used, in which case arranging the switches into a binary tree structure would provide inherent decoding using only the digital input signal.
Aside from simplicity in design, another major benefit associated with using resistor string DACs as opposed to other types of DACs is that resistor string DACs are intrinsically monotonic (as long as the switching elements are functioning properly). Accordingly, an increase in the digital input signal results in an increased analog output voltage, while a decrease in the digital signal results in a decreased analog output voltage.
A significant drawback associated with using resistor string DACs, however, is that the linearity of the analog output voltages corresponding to different digital input signals is limited by the precision with which the voltage division is accomplished. As the resolution of the resistor string DAC increases, the number of resistors increases exponentially, increasing the likelihood that the resistors being used will have reduced precision. Moreover, as the number of binary bits in the digital signal increases, the quantization step size decreases for any given reference voltage being used. Accordingly, the voltage taps provided by the resistor string of the resistor string DAC become much closer as the resolution of the DAC increases, thus increasing the requirements for accurately matched resistors.
Accurate resistor matching can also be a problem in another type of DAC, the interpolating amplifier DAC, which operates using the principle of a segmented DAC and is explained in greater detail below. Because interpolating amplifier DACs may also utilize resistor strings in order to provide voltage taps (for providing analog output voltages), the accuracy associated with the resistor matching in the resistor string or strings being used affects the quality (e.g., linearity) of the analog output voltages.
Due to various technological limitations, the matching of the resistor string resistors for larger resolution DACs becomes extremely difficult. One factor that limits the resistor matching, and therefore the accuracy of voltage division by the resistor string, is the introduction of error gradients (e.g., linear error gradients). Persons skilled in the art will appreciate that the phrase “error gradients” used herein may refer to a single error gradient, or a plurality of error gradients that produce deviations in resistor values as described below.
Fabrication time linear error gradients may be introduced, for example, during the resistive network fabrication process. These linear error gradients, which in some instances are the result of imperfect processing during the fabrication of resistors, may be due to a number of different factors. For example, the imperfect processing of resistors may be due in part to variations in either the doping density or fabricated resistor widths, or both. Additional factors which may lead to the introduction of linear error gradients include, for example, variations in the resistor lengths as determined by contact openings and the thickness of the resistive material layer. Accordingly, variations in the sheet resistance and geometry of the resistive materials cause imperfections during the fabrication of resistors. Moreover, variations in contact resistance may also contribute to the introduction of linear error gradients.
Linear error gradients may also be introduced at some point other than the resistive network fabrication process. For example, resistors used in resistor string DACs or interpolating amplifier DACs may be subject to thermal linear error gradients. In this case, variations in the temperature conditions surrounding the various resistors of a resistor string may result in the resistors being subject to undesirable deviations in resistor values.
In view of the foregoing, it would be desirable to provide various resistor string and interpolating amplifier DACs that are at least partially insensitive to the effects of error gradients.